This is a key orbital dynamics principle of which most people are blissfully unaware: going “faster” doesn’t actually make you go faster, it makes you go HIGHER. In practical terms, this means that if you’re in a spaceship trailing the ISS in the same orbit around earth (or are trying to get Cassini to catch up with a moon of Saturn, or whatever), you can’t just “hit the gas” because you’ll end up in a higher, slower orbit. Instead, you have to “hit the brakes” to get to a slightly lower, faster orbit in order to catch up. It is not at all an intuitive process, and while it can be learned and done without computer controlled systems, it is a cold, cast-iron bitch.